On two special functions, generalizing the Mittag-Leffler type function, their properties and applications

On two special functions, generalizing the Mittag-Leffler type function, their properties and applications

Two special functions, concerning Mittag-Leffler type functions, are studied. The first is the modification of generalized Mittag–Leffler function, which was introduced by A. A. Kilbas and M. Saigo; the second is the special case of the first one. The relation of these functions with some elementary...

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Main Author: E. N. Ogorodnikov
Format: Article
Language:English
Published: Samara State Technical University 2012-03-01
Series:Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki
Online Access:http://mi.mathnet.ru/eng/vsgtu1067
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spelling doaj-5a1a4cfd5e2847ad955bad473f14503c2020-11-25T02:48:23ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812012-03-011(26)526510.14498/vsgtu1067 On two special functions, generalizing the Mittag-Leffler type function, their properties and applications E. N. OgorodnikovTwo special functions, concerning Mittag-Leffler type functions, are studied. The first is the modification of generalized Mittag–Leffler function, which was introduced by A. A. Kilbas and M. Saigo; the second is the special case of the first one. The relation of these functions with some elementary and special functions and their role in solving of Abel–Volterra integral equations is indicated. The formulas of the fractional integration and differentiation in sense of Riemann–Liouville and Kober are presented. The applications to Cauchy type problems for some linear fractional differential equations with Riemann-Liouville and Kober derivatives are noticed. http://mi.mathnet.ru/eng/vsgtu1067
collection DOAJ
language English
format Article
sources DOAJ
author E. N. Ogorodnikov
spellingShingle E. N. Ogorodnikov
On two special functions, generalizing the Mittag-Leffler type function, their properties and applications
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki
author_facet E. N. Ogorodnikov
author_sort E. N. Ogorodnikov
title On two special functions, generalizing the Mittag-Leffler type function, their properties and applications
title_short On two special functions, generalizing the Mittag-Leffler type function, their properties and applications
title_full On two special functions, generalizing the Mittag-Leffler type function, their properties and applications
title_fullStr On two special functions, generalizing the Mittag-Leffler type function, their properties and applications
title_full_unstemmed On two special functions, generalizing the Mittag-Leffler type function, their properties and applications
title_sort on two special functions, generalizing the mittag-leffler type function, their properties and applications
publisher Samara State Technical University
series Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki
issn 1991-8615
2310-7081
publishDate 2012-03-01
description Two special functions, concerning Mittag-Leffler type functions, are studied. The first is the modification of generalized Mittag–Leffler function, which was introduced by A. A. Kilbas and M. Saigo; the second is the special case of the first one. The relation of these functions with some elementary and special functions and their role in solving of Abel–Volterra integral equations is indicated. The formulas of the fractional integration and differentiation in sense of Riemann–Liouville and Kober are presented. The applications to Cauchy type problems for some linear fractional differential equations with Riemann-Liouville and Kober derivatives are noticed.
url http://mi.mathnet.ru/eng/vsgtu1067
work_keys_str_mv AT enogorodnikov ontwospecialfunctionsgeneralizingthemittaglefflertypefunctiontheirpropertiesandapplications
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